Finite Group Databasebeta

← #14742999

Subgroups — #14742999

Order 2816.

670 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079777C211yesmaximal, characteristic, complemented
2#13079767C211yesmaximal, characteristic, complemented
3#13079748C211yesmaximal, characteristic
4#13079572C211yesmaximal, characteristic
5#13079564C211yesmaximal, characteristic, complemented
6#13068294C211yesmaximal, characteristic, complemented
7#13068292C211yesmaximal, characteristic, complemented
8#13068289C211yesmaximal, characteristic, complemented
9#13068278C211yesmaximal, characteristic, complemented
10#13068266C211yesmaximal, characteristic, complemented
11#13068261C211yesmaximal, characteristic, complemented
12#13068233C211yesmaximal, characteristic, complemented
13#13068227C211yesmaximal, characteristic, complemented
14#13066916C211yesmaximal, characteristic, complemented
15C11×#3226C211yesmaximal, characteristic
16C11×#532C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18#10623001C2211yescharacteristic
19#10623001C2211yescharacteristic
20C11×#500C2211yescharacteristic
21C11×#500C2211yescharacteristic
22C11×#486C2211yescharacteristic
23C11×#486C2211yescharacteristic
24C11×#480—22no—
25C11×#474—22no—
26C11×#431C2211yescharacteristic
27#10622852—22no—
28#10622841—22no—
29#10622706C2211yescharacteristic
30#10622706C2211yescharacteristic
31#10622705C2211yescharacteristic
32#10622705C2211yescharacteristic
33#10622705C2211yescharacteristic
34#10622704—22no—
35#10622703—22no—
36#10622694C2211yescharacteristic
37#10622694C2211yescharacteristic
38#10622694C2211yescharacteristic
39#10622692C2211yescharacteristic
40#10622691C2211yescharacteristic
41#10622691C2211yescharacteristic
42#10622691C2211yescharacteristic
43#10622689C2211yescharacteristic
44#10622683C2211yescharacteristic
45#10622683C2211yescharacteristic
46#10622683C2211yescharacteristic
47#10622667—22no—
48#10622648—22no—
49#10622622—22no—
50#10622583—22no—
51#10622538C2211yescharacteristic
52#10622538C2211yescharacteristic
53#10622442—22no—
54#10622336—22no—
55#10622295C2211yescharacteristic
56#10622294C2211yescharacteristic
57#10622294C2211yescharacteristic
58#10622293C2211yescharacteristic
59#10622093C2211yescharacteristic
60#10622092C2211yescharacteristic
61#10622092C2211yescharacteristic
62C8×C11⋊C8C2211yescharacteristic
63C2×C11×#41—21no—
64C22×Q8×C11—21no—
65C11×C4⋊Q8—21no—
66C11×C4⋊Q8—21no—
67C11×C4⋊Q8—21no—
68C11×C4⋊Q8C2311yescharacteristic
69C11×C4⋊Q8C2311yescharacteristic
70C11×C4⋊Q8C2311yescharacteristic
71C11×#127C2311yescharacteristic
72C11×#124—21no—
73C11×#121—21no—
74C11×#121—21no—
75C4×D4×C11—21no—
76C4×D4×C11—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C42×C11C2311yescharacteristic
80C2×#4326—22no—
81C2×#4326—22no—
82C2×#4326—22no—
83C2×#4324—22no—
84#66979—21no—
85#66979—21no—
86#66977—21no—
87#66977—21no—
88#66977—21no—
89#66977—21no—
90#66923—21no—
91#66923—21no—
92#66922C2311yescharacteristic
93#66922C2311yescharacteristic
94#66922C2311yescharacteristic
95#66922C2311yescharacteristic
96C4×Dic22—21no—
97C4×Dic22—21no—
98C4×Dic22—21no—
99C4×Dic22—21no—
100C11×#107—22no—
101C11×#107—22no—
102C11×C4⋊C8D412yes—
103C11×#102—22no—
104C11×#102—22no—
105C11×C22⋊C8D412yes—
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108#66899—22no—
109#66899—22no—
110#66899—22no—
111#66896—22no—
112#66896—22no—
113#66896—22no—
114C22⋊(C11⋊C8)D412yes—
115C22⋊(C11⋊C8)D412yes—
116#66882—22no—
117#66881—22no—
118#66880—22no—
119#66880—22no—
120#66874—22no—
121#66874—22no—
122#66872—22no—
123#66871—22no—
124#66871—22no—
125#66871—22no—
126C4⋊(C11⋊C8)D412yes—
127C4⋊(C11⋊C8)D412yes—
128C4×C11⋊C8C2311yescharacteristic
129C4×C11⋊C8C2311yescharacteristic
130C4×C11⋊C8C2311yescharacteristic
131C4×C11⋊C8C2311yescharacteristic
132#19744—111nomaximal, Sylow
133C11×#41—82no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—41no—
138C2×Q8×C11—82no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—41no—
143C22×C4×C11—41no—
144C22×C4×C11—41no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×C8×C11C2×D412yes—
153C2×C8×C11C2×D412yes—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—41no—
161C11×C4⋊C4—41no—
162C11×C22⋊C4—41no—
163C11×C22⋊C4—41no—
164C42×C11C2×D411yescharacteristic
165C42×C11C2×D411yescharacteristic
166C42×C11C2×D411yescharacteristic
167C42×C11C2411yescharacteristic
168C22⋊Dic11—41no—
169C22⋊Dic11—41no—
170#4326—82no—
171#4326—82no—
172#4326—82no—
173#4324—82no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182Dic11⋊C4—41no—
183Dic11⋊C4—41no—
184Dic11⋊C4—41no—
185Dic11⋊C4—41no—
186C4×Dic11—41no—
187C4×Dic11—41no—
188C2×C11⋊C8C2×D412yes—
189C2×C11⋊C8C2×D412yes—
190C2×C11⋊C8C2×D412yes—
191C2×C11⋊C8C2×D412yes—
192#3231—111no—
193#3230—111no—
194#3228—111no—
195#3226D1111yescharacteristic
196#3210—111no—
197#3209—111no—
198#1723—111no—
199#1723—111no—
200#1722—111no—
201#1720—111no—
202#1719—111no—
203#1718—111no—
204#1713—111no—
205#1711—111no—
206#1454—111no—
207C23×C11—41no—
208C23×C11#12711yescharacteristic
209Q8×C11—42no—
210Q8×C11—42no—
211Q8×C11—42no—
212Q8×C11—82no—
213D4×C11—42no—
214D4×C11—42no—
215D4×C11—42no—
216D4×C11—82no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—82no—
224C2×C4×C11—82no—
225C2×C4×C11#12711yescharacteristic
226C2×C4×C11#12711yescharacteristic
227C2×C4×C11#12711yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235Dic22—42no—
236Dic22—42no—
237Dic22—42no—
238Dic22—42no—
239C8×C11—22no—
240C8×C11—22no—
241C11⋊C8—22no—
242C11⋊C8—22no—
243C11⋊C8—22no—
244C11⋊C8—22no—
245#533—111no—
246#533—111no—
247#532C2×D1111yescharacteristic
248C2×C4⋊Q8C2×D1111yescharacteristic
249#500—111no—
250#500—111no—
251#500—111no—
252#500—111no—
253#500C2×D1111yescharacteristic
254#500C2×D1111yescharacteristic
255#498—111no—
256#498—111no—
257#494—111no—
258#494—111no—
259#494—111no—
260#492—111no—
261#487—111no—
262#487—111no—
263#487—111no—
264#487—111no—
265#487—111no—
266#487—111no—
267#487—111no—
268#486—111no—
269#486—111no—
270#486—111no—
271#486C2×D1111yescharacteristic
272#486C2×D1111yescharacteristic
273#485—222no—
274#484—222no—
275#482—222no—
276#480—22no—
277#479—222no—
278#478—222no—
279#477—222no—
280#474—22no—
281#464—222no—
282#462—222no—
283#452—222no—
284#451—222no—
285#431—111no—
286#431—111no—
287#431C2×D1111yescharacteristic
288#322—111no—
289#322—111no—
290#322—111no—
291C82—111no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11C2×#12711yescharacteristic
299C4×C11—21no—
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—81no—
303C4×C11—81no—
304C4×C11—81no—
305C4×C11#57612yes—
306C4×C11#57812yes—
307C4×C11#57812yes—
308Dic11—81no—
309Dic11—81no—
310Dic11—81no—
311Dic11—81no—
312C2×#41—21no—
313C22×Q8—21no—
314C2×Q16—222no—
315C2×Q16—222no—
316C2×Q16—222no—
317C2×SD16—222no—
318C4⋊Q8—21no—
319C4⋊Q8—21no—
320C4⋊Q8—21no—
321C4⋊Q8—111no—
322C4⋊Q8—111no—
323C4⋊Q8—111no—
324C4⋊Q8—111no—
325C4⋊Q8C22×D1111yescharacteristic
326C4⋊Q8C22×D1111yescharacteristic
327C4⋊Q8C22×D1111yescharacteristic
328#127C22×D1111yescharacteristic
329#125—221no—
330#125—221no—
331#124—21no—
332C22⋊Q8—221no—
333C22⋊Q8—221no—
334C22⋊Q8—221no—
335C22⋊Q8—221no—
336#121—21no—
337#121—21no—
338C4×Q8—221no—
339C4×Q8—221no—
340C4×Q8—221no—
341C4×Q8—221no—
342C4×D4—21no—
343C4×D4—21no—
344#117—221no—
345#117—221no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C42C22×D1111yescharacteristic
349#107—22no—
350#107—22no—
351#107—222no—
352#107—222no—
353#107—222no—
354#107—222no—
355#106—222no—
356#106—222no—
357C4⋊C8—112no—
358C4⋊C8—112no—
359C4⋊C8C22⋊D1112yes—
360#103—222no—
361#103—222no—
362#103—222no—
363#103—222no—
364#103—222no—
365#103—222no—
366#103—222no—
367#102—22no—
368#102—22no—
369#102—222no—
370#102—222no—
371#102—222no—
372C22⋊C8—112no—
373C22⋊C8—112no—
374C22⋊C8C22⋊D1112yes—
375C4×C8—111no—
376C4×C8—111no—
377C4×C8—111no—
378C4×C8—111no—
379C4×C8C22×D1111yescharacteristic
380C4×C8C22×D1111yescharacteristic
381C2×C11—41no—
382C2×C11—161no—
383C2×C11#315511yescharacteristic
384C2×C11#315611yescharacteristic
385C2×C11#315611yescharacteristic
386#41—82no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—41no—
391C2×Q8—82no—
392C2×Q8—221no—
393C2×Q8—221no—
394C2×Q8—221no—
395C2×Q8—221no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4D4×D1111yescharacteristic
403C22×C4D4×D1111yescharacteristic
404C22×C4C2×C22⋊D1111yescharacteristic
405Q16—882no—
406Q16—882no—
407Q16—882no—
408SD16—882no—
409C2×C8—112no—
410C2×C8—112no—
411C2×C8—112no—
412C2×C8—112no—
413C2×C8C2×C22⋊D1112yes—
414C2×C8C2×C22⋊D1112yes—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—221no—
424C4⋊C4—221no—
425C4⋊C4—221no—
426C4⋊C4—221no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4—221no—
430C4⋊C4—221no—
431C4⋊C4—441no—
432C4⋊C4—441no—
433C4⋊C4—441no—
434C4⋊C4—441no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—441no—
438C22⋊C4—441no—
439C42—441no—
440C42—441no—
441C42D4×D1111yescharacteristic
442C42D4×D1111yescharacteristic
443C42C2×C22⋊D1111yescharacteristic
444C42C23×D1111yescharacteristic
445C11#1974411yescharacteristic, complemented, Sylow
446C23—41no—
447C23#6699311yescharacteristic
448Q8—42no—
449Q8—42no—
450Q8—42no—
451Q8—82no—
452Q8—442no—
453Q8—442no—
454Q8—442no—
455Q8—442no—
456D4—42no—
457D4—42no—
458D4—42no—
459D4—82no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—82no—
467C2×C4—82no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4—441no—
472C2×C4#6699311yescharacteristic
473C2×C4#6699311yescharacteristic
474C2×C4#6699311yescharacteristic
475C2×C4C2×D4×D1111yescharacteristic
476C2×C4C2×D4×D1111yescharacteristic
477C2×C4C22×C22⋊D1111yescharacteristic
478C8—22no—
479C8—22no—
480C8—222no—
481C8—222no—
482C8—222no—
483C8—222no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22C2×#6699311yescharacteristic
491C4—21no—
492C4—21no—
493C4—21no—
494C4—81no—
495C4—81no—
496C4—81no—
497C4—881no—
498C4—881no—
499C4—881no—
500C4—881no—
501C4#1062328812yes—
502C4#1062331012yes—
503C4#1062336912yes—
504C2—41no—
505C2—161no—
506C2#1307909711yescharacteristic
507C2#1307910711yescharacteristic
508C2#1307910911yescharacteristic
subgroupG/H
centerC22C2×#66993
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3226C2
socleC22×C11C2×#127
prime radicalC11×#532C22
hypercenter#3226D11
hypocenterC11#19744
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3226

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13079777C2semidirect
2. #13079767C2semidirect
5. #13079564C2semidirect
6. #13068294C2semidirect
7. #13068292C2semidirect
8. #13068289C2semidirect
9. #13068278C2semidirect
10. #13068266C2semidirect
11. #13068261C2semidirect
12. #13068233C2semidirect
13. #13068227C2semidirect
14. #13066916C2semidirect
445. C11#19744semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130797772
#130797672
#130797482
#130795722
#130795642
#130682942
#130682922
#130682892
#130682782
#130682662
#130682612
#130682332
#130682272
#130669162
C11×#32262
#1974411